Isotropic Quadratic Forms, Diophantine Equations and Digital Signatures

Martin Feussner; Igor Semaev

Paper 2024/679

Isotropic Quadratic Forms, Diophantine Equations and Digital Signatures

Martin Feussner

, University of Bergen

Igor Semaev, University of Bergen

Abstract

This work introduces DEFI - an efficient hash-and-sign digital signature scheme based on isotropic quadratic forms over a commutative ring of characteristic 0. The form is public, but the construction is a trapdoor that depends on the scheme's private key. For polynomial rings over integers and rings of integers of algebraic number fields, the cryptanalysis is reducible to solving a quadratic Diophantine equation over the ring or, equivalently, to solving a system of quadratic Diophantine equations over rational integers. It is still an open problem whether quantum computers will have any advantage in solving Diophantine problems.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: digital signatures isotropic quadratic forms Diophantine equations
Contact author(s): martin feussner @ uib no
igor semaev @ uib no
History: 2024-05-06: approved; 2024-05-03: received; See all versions
Short URL: https://ia.cr/2024/679
License: CC BY

BibTeX

@misc{cryptoeprint:2024/679,
      author = {Martin Feussner and Igor Semaev},
      title = {Isotropic Quadratic Forms, Diophantine Equations and Digital Signatures},
      howpublished = {Cryptology ePrint Archive, Paper 2024/679},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/679}},
      url = {https://eprint.iacr.org/2024/679}
}